Ultimate strength of cold-formed steel z-purlins

Transcription

1 Missouri University of Science and Technology Scholars' Mine Center for Cold-Formed Steel Structures Library Wei-Wen Yu Center for Cold-Formed Steel Structures Ultimate strength of cold-formed steel z-purlins M. A. A. Razak Teoman Peköz Follow this and additional works at: Part of the Structural Engineering Commons Recommended Citation Razak, M. A. A. and Peköz, Teoman, "Ultimate strength of cold-formed steel z-purlins" (1980). Center for Cold-Formed Steel Structures Library This Report - Technical is brought to you for free and open access by Scholars' Mine. t has been accepted for inclusion in Center for Cold-Formed Steel Structures Library by an authorized administrator of Scholars' Mine. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact scholarsmine@mst.edu.

2 Department of Structural Engineering School of Civil and Environmental Engineering Cornell University Report No PROGRESS REPORT ULTMATE STRENGTH OF COLD-FORMED STEEL Z-PURLNS by M.A.A. Razak Teoman Pekoz, Project Director A Research Project Sponsored by the American ron and Steel nstitute and the Metal Building Manufacturers Association thaca, New York February 1980

3 PREFACE This progress report is based on a thesis presented to the faculty of the Graduate School of Cornell University for the degree of Master of Science. The sponsorship of the American ron and Steel nstitute and of the Metal Building Manufacturers Association as well as the cooperation of the committees of the sponsors are gratefully acknowledged.

4 TABLE OF CONTENTS CHAPTER Page 1. NTRODUCTON General Previous Studies. Objectives of this Study. 2. STABLTY ANALYSS ntroduction. 2.2 Stabili ty Analysis Portion of Compression Flange Acting as a Column The Effect of Torsional nstability Stability Condition Simplification of Stability Condition Design Approximation for Torsional Reduction Factor EXPERMENTAL NVESTGATON General General Procedure. Vacuum Tests. Beam Test s. Rotational Restraint Tests. Shear Rigidity Tests. Ma t eria1 Propertie Section Dimensions. Discussion of Test Results Tests Results Discussion of Vacuum Test Results Discussion of Beam Test Results. 4. ANALYSS OF RESULTS General. Background for Evaluation of Results AS Design Specification Discussion of Design Specification Adequacy of Compression Flanges. Evaluation of Results Test Ultimate Loads Test Ultimate Stresses Test Ultimate Rotations Rotational Restraint Factor, F v

5 CHAPTER Page Shear Rigidity of Panels nitial Sweeps of Compression Flanges Ultimate Loads General Computations Based on Full Widths of Flanges Computations Based on Effective Widths CArS) Computations Based on Desmond's Flange and Stiffener Adequacy Requirements Discussion of Analysis Summary CONCLUSON Summary of Results Recommendations Suggestions for Future Work 54 APPENDCES 55 A. Location of Shear Center for Equivalent Column 55 B. Design Method for Edge Stiffened Element 57 REFERENCES 63 TABLES FGURES 78 vi

6 LST OF TABLES TABLE 3.1 Material Properties (Tensile) Page 3.2 Average Pur1in Dimensions Summary of Test Results Test Ultimate Stresses Test Ultimate Rotations and F Values Rotational Deformation of Pur1in Web 4.4 Yield and Ultimate Stresses Summary of Analysis Types Comparison of Observed and Computed Ultimate Loads in Vacuum Tests Comparison of Observed and Computed Ultimate Loads in Beam Tests Minimum Stiffener Requirement According to AS Effective Widths of Compression Flanges and Lip-Stiffeners (Desmond Method) vii

7 LST OF FGURES FGURE 2.1 Mode of Buckling Page 2.2 Force Normal to Buckled Flange Force Normal to Buckled Web Three Possible Types of Supporting Elastic Frame for Equivalent Column The Effect of the Ratio blh on Rand S for Cas e T vs. Length Curves Vacuum Test Setup Section of Vacuum Test Setup. 3.3 Views Showing Beam Test Setup Details of Beam Test Z-Section Dimensions Setup nitial Sweeps of Compression Flanges in Vacuum Test s : Panel Cross-Section. nitial Sweeps of Compression Flanges in Beam Tests. Location of Strain Gages F Test: Diaphragm-Braced Pur 1 in F Test: Channel-Braced Purlin Shear Rigidity Test Setup Local Buckles in Test V and VS. Local Buckles in Test Bl, B2 and B3. Local Buckle in Test V2. Local Buckles in Test V4 and B viii

8 FGURE Local Buckles in Test V3 Local Buckles in Test V6 and B4 and B7 Page 4.1 Compression Area of Z-Section Displacement Sign Convention Load vs. Strain (Test VS) Load vs. Strain (Test V2) Load vs. Strain (Test V4) Load vs. Strain (Test V3) Load vs. Strain (Test V6) Load vs. Strain (Test B3) Load vs. Strain (Test Bs) Load vs. Strain (Test B6) Load vs. Strain (Test B4) Load vs. Strain (Test B7) Comparison of Stresses (Pur1in Type A) Comparison of Stresses (Pur1in Type B) Comparison of Stresses (Pur1in Type C) Comparison of Stresses (Pur1in Type D) Comparison of Stresses (Pur1in Type E) 4.18 Vacuum Tests: Load-Rotation Curves Beam Tests: Load-Rotation Curves Rotational Restraint Tests (Diaphragm-Braced Pur1ins): Moment-Rotation Curves Rotational Restraint Tests: Pur1in Type E (Diaphragm-Braced Pur1ins): Moment-Rotation Curves F Tests (Channel-Braced Pur1ins): Moment-Rotation Curves ix

9 FGURE Hit vs. F Shear Rigidity Test: Load-Deflection Curve Page A.l Location of Shear Center for Equivalent Column. B.l Typical Edge Stiffened Elements x

10 CHAPTER 1 NTRODUCTON 1.1 General Cold-formed steel structures are being widely used in various forms of construction such as industrial plants, gymnasiums, hangars and metal buildings. One important feature of metal building construction is the use of light gage roof panels connected to purlins, particularly of the Z-section. This section is, besides the channel-section, the simplest twoflange section which can be produced by cold-forming. The purlins have span lengths of 20 to 25 feet, generally made continuous over the building rigid frames by nesting. Construction details vary from manufacturer to manufacturer. The purlins available would typically have prepunched holes for connection of various types of bracings, overlapping connections, etc. 1.2 Previous Studies Studies involving such purlin-panel assemblies have been carried out by a limited number of investigators. Cornell University carried out a series of studies on channel and Z section behavior as regards lateral, flexural, torsional and flexural-torsional buckling. t is not the intention of this particular study to investigate any of such buckling modes as these have been well reported in the various Cornell University reports referenced and others. 1

11 2 A particularly important study on laterally unbraced compression flanges is that of Douty6 undertaken at Cornell University. Section 3, Part of the American ron and Steel nstitute CAS) Cold-Formed Steel Design Manual l was formulated based on Douty's design approach. t is noted that this approach was intended for sections which have overall lateral stability. This study is presented in Chapter 2. Douty's approach as formulated in the AS Design Manual is frequently used for calculating the allowable stress on a beam in which the tension flange is continuously braced while the compression flange is either free or braced at intervals along its length. This would be the case when a purlin is subjected to an uplift load, braced continuously by the diaphragm strength of the roof panel. n a survey undertaken by Ellifritt 7 of the Metal Building Manufacturers Association, there was observed considerable variation in the computed allowable stresses. He attributed this almost exclusively to the selection of the spring constant, 8, which represents the rotational restraint of the purlinpanel assembly. Hence, the accurate determination of 8 is critical in predicting the ultimate load capacity of the purlins. Another important Cornell study was on diaphragm-braced channel and Z-sections by Celebi. 4 He studied the theoretical basis for the design of diaphragm-braced thin-walled channel and Z-section beams and obtained the solution to the differential equation involved. A computer program, coded based on

12 3 his investigations and conclusions, is used by the metal building industry to check their design recommendations. One significant aspect of this study is the consideration of both the shear rigidity and the rotational rigidity of the diaphragm in bracing of purlins. A follow-up of Celebi's study was done by Pekoz. ll developed further the computer program coded by Celebi 4 and conducted tests on three span continuous diaphragm-braced purlin assemblies. computer program solutions. The test results were correlated with the A significant study on the strength of elastically stabilized beams was done by Haussler. S n many respects, this study is comparable to that of Douty Objectives of this Study This study will attempt to establish by full-scale testing of diaphragm-braced purlins under simulated uplift loads a reliable failure criteria of such purlins. He The current AS Design Manual, particularly that of Section 3, Part, shall be employed as a suitable foundation for such a criteria. Further inputs shall be considered from the differential equation solution as coded in a computer program by Celebi. study will particularly look into the problem of the rotational restraint factor, F, from which the spring constant, 8, is computed. The Chapter 2 will detail the analytical studies as presented by Douty6 on the stability analysis of laterally unbraced compression flange. Chapter 3 presents the details of the experi-

13 4 mental program with particular emphasis on what is called the vacuum test procedure for testing the purlins. Analysis of the results are done in Chapter 4, followed by conclusions, design recommendations and suggestions for future work in Chapter S.

14 6 2.2 Stability Analysis Portion of Compression Flange Acting as a Column Considering the simple case of the U-shaped beams, when the compression flange is subjected to the critical bending forces cr cr A f, where cr cr is the critical stress and A f is the area of the flange, the component normal to the deflected flange is A f d 2 x /dz 2, where x a a is the displacement of the top flange in the x-direction (see Figure 2.2). The differential equation for the deflection of the flange as a beam is = 2.1 The lateral force component on a unit length of the deflected web is crt d 2 x/dz 2 w, where cr is assumed to be a linear function of the distance from the neutral axis, i.e., directly proportional to y, and t is the thickness of the web. Figure w 2.3 shows the distribution of the lateral force on the web. The lateral force in the tension region C is directed opposite t to the direction of displacement while in the compression region C c ' it is directed in the direction of displacement. The lateral force in the web is transmitted to the compression flange and the magnitude of the total force per unit length of beam is obtained by taking moments about the base of the web giving the following result: = 2.2

15 7 where R a = total lateral force transmitted to the compression flange by the buckled web. A web = area of web. C c = distance from the neutral axis to the extreme compression fiber. C t = distance from the neutral axis to the extreme tension fiber. The equation of equilibrium of the compression flange then would be: + (J cr 2.3 and the corresponding nontrivial eigenvalue leads to: (J cr 2.4 where r is the radius of gyration of the flange together with a portion of the web of depth d(3c c - C t ) / 12C c ' where d is the depth of the beam. This is the portion of the web which, along with the compression flange, can be considered as the column subjected to buckling The Effect of Torsional nstability Stability Condition The analysis in Section is for the type of column

16 8 supported on an elastic foundation where the elastic support is provided by the remaining portion of the web and the tension flange acting together as an elastic frame. The effect of torsional weakening in the combined flexural-torsional stability of the effective column is considered by using the theorem of minimum potential energy. The following analysis is based on the analysis for the stability of the upper chord of a pony truss bridge presented by Bleich. 3 The change in the entire potential energy of the system, U is given by: U = V + V z + U w = } f a L L CC u - 2Czu<p + C3<P )dz P J a L J [Cu,)2 + 2y u'<p' + C-!:) C<p,)2]dz a where P = axial load on the effective column. U = the change in the entire potential energy of the system consisting of the effective column and its supporting elastic frame. V = strain energy accumulated in the bent and twisted column. V 2 = strain energy of the deflected supporting frame.

17 9 U w = the change of potential energy of the external forces acting on the system. y = moment of inertia of the column about its vertical y axis. u = horizontal displacement of the shear center. ~ = rotation of the column. J Yo = torsional rigidity of the column. = vertical distance between the shear center and the centroid of the column. p = polar moment of inertia of the column about its shear center. = warping constant. = o~/(ouo~ - O~~) 2 = 0u~/(ouo~ - 0u~) = 0u/(ouo~ - a~~) = horizontal displacement of the shear center due to a unit load. au~ = horizontal displacement of the shear center due to a unit moment. a~ = rotation of column due to a unit moment. To minimize the integral U so that au = 0, the following Euler-Lagrange differential equations must be satisfied: 2.6a

18 10 where af d af d 2 af a az (a<ii') + dz 2 (a<j>l) = L U = f F(z,u,u',u",<j>,<j>',<j>")dz 0 0 Z.6b To satisfy the boundary conditions, substitute the eigenfunctions u = Al Sin nrrz/l <j> = AZSin nrrz/l where n = 1,Z,3,... A nontrivial solution can exist only if the determinant of the coefficients of Al and A Z is zero (A and A Z are indeterminate): Pcr 1+1.l --- n P n where Z.7 L = length of column without elastic foundation. Expanding Z.7 gives the following quadratic equations: P C 3 C z (-E. yz)( cr)z [- l.l n +...E. (1 + l.l n ) + Zy S" lln A o~ C l A 0 C w LZGJ Per C Cz Z + + ] + [ 3 ( ) y n 2 1T 2 E P (C 1.1 n ) n S- n n 1 y

19 Equation 2.8 is the general equation of torsionalflexural stability for a column on an elastic foundation if a Winkler foundation, i.e., closely spaced springs, is assumed. Although the support provided by that part of the beam considered to be the elastic foundation is continuous, the difference is significant only for very short columns when compared with that of closely spaced discrete springs. The Winkler foundation is more conservative as it is less firm than that provided by a continuous foundation Simplification of Stability Condition Equation 2.8 can be expressed in a general form as: 2.9 Numerical investigations done by Douty on various shapes as indicated in Reference 6 show that A is insignificant when compared with Band C for short column length. t becomes more insignificant as the column length increases since A remains static while Band C increases with length. Thus, the second order term of (Pcr/P n ) general stability equation to: can be neglected reducing the C 3 C 2 2 C + GJ P Cl (1 + lln)lln - (- lln) +~ (1 + lln) (1 + C lln) l y P cr = n P n C 3 C C W GJ + ~ (1 + lln) + 2y ~ + + C lln l A 0 C l n y P 2.10 n

20 12 Winter 12 published the following equations for determining the strength of a column on an elastic foundation which buckle flexurally: for 2.11 p ~ ~ = (0.6 + ~ /~) e e for 2.12 where P cr = critical load of equivalent column. P e = Euler critical load = T 2 E/L 2 S = spring constant = lid D L = lateral deflection of the column centroid due to a unit force applied to the web at the level of the column centroid. = unbraced length of equivalent column Equation 2.10 can be manipulated and rewritten as: 1 + C3 (C2) Cw + GJ C L2 C:- C C w Z:-p GJ T n Cl n y Pn l_ll_n~_c..;;l;;..."-,,.--n y,--_p..;;n~( 1 ) x C -f 2 (1 + lln) + 2y -lln 1 + C C 3 + w + GJ Cl n y P n 0 C l

21 13 Comparison of Equation 2.13 with Equation 2.11 shows that the former is completely analogous to the latter if S is the following expression: GJ P n) C l 2.14 The additional multiplier within the second bracket of Equation 2.13 can be regarded as a reduction factor due to the torsional weakness of the cross-section. The value of Cw/ y is generally small in relation to the other terms. Hence, Seq can be reduced to: 2.15 For short columns, it can be shown that S eq is a function of L and the torsional constant J. limit of Equation 2.15 is: As L increases, the asymptotic C l C 3 - C 2 Seq = 2 C which in turn reduces to: Seq = 1/0 u 2.17 This is the modulus of the elastic foundation which restraints the deflection perpendicular to the web of the beam. Douty's study showed that S = 1/0 eq u is an accurate approximation for longer columns, and conservative to use for short columns. Thus, Equations 2.11 and 2.13 are identical except for the term

22 14 in the second bracket of Equation 2.13 which will be called the torsional reduction factor: T = 1+ -: ( Design Approximation for Torsional Reduction Factor t is necessary to reduce Equation 2.18 to a simple enough expression applicable to cold-formed light gage columns on an elastic foundation. The expression for T can be simplified to: T = -l: Equation 2.19 is justified from consideration of the terms C and GJ/P which are negligible when compared with w y n (C3/Cl)~n' for typical light gage beams. From Equation 2.12, the length of one half wave in the asymptotic limit is L' = ~4/E8. The total length is nl l Substituting for n in ~n = CL n ~ E and 8 = (C l C 3 - C 2 )/C 3, gives the asymptotic form of T:

23 15 From consideration of the three common types of elastic support configurations found in light gage steel construction (see Figure 2.4), C l, C 2 and C 3 can be simplified. C l ' C z and C 3 are constants, each of which involves the three possible displacements caused by a unit moment and a unit force applied to the column on elastic support. The three cases considered, Case, Case and Case correspond to the elastic support configuration as shown in Figure 2.4. The deflections at the top of the web produced by a unit moment and unit force at that point on a unit length of beam for each of the three cases are: Case u u</> o</> h 3 + hzb h Z hb h b + + 3El w 2El f ZE ZEl f El w 2El f w Case h 3 + hzb h Z hb h b + + 3E 4El f 2El w 4El f El w 4El f w Z.Zl Case h 3 hzb h Z hb + h b + + 3E w 12El f ZE lzel f El w lzel w f Substituting au, u</>' o</> in the expressions for C l ' C z and C 3, Equation Z.20 can be simplified to: For Case (and for w = f) : T a = R 1 Z.22 Yo 1 + h2~ + S 11 where R = (%) + 9(~)Z (2 + 3 *) 2

24 16 s = b (1 + *) b n Expressions for Cases and can be easily derived. The expressions obtained however are still too complex and cumbersome for design use, although sufficient for detailed structural analysis. Douty showed, however, that Rand S become asymptotic to 1.0 and 2.0, respectively, as the ratio blh increases (see Figure 2.5). He showed that it is conservative and expedient to consider the case b = h. Thus, further simplifying for the three cases with b = h: Case : T a = Case : T a = Yo ~+ h 2 A h yo E.+ h 2 A h 2.23a 2.23b Case : T a = 1 2.8yo E.+ h 2 A h 2.23c From examination of the term ~n in Equation 2.19, T is highly dependent on L for low values of L. ~n (= c1l4/n4~4ey) becomes dominant as Ln increases. At the transition point: (n = 1) 2.24 For Case, C l is computed using the applicable values of au, o4> and 0 u4> to give:

25 , ) t'l :,!l :h b h :1; i: 0 r b h.: nd t. t 3/ 1:.... "11m Douty did a numerical investigation by computer of 2.25 Equation :.19 for several shapc~ repre~enting Case for vary- 1n, lengths and n 1 to 4 for each of the length. Results for one shape ~ith the dimen~lon~ lndic3tcd is as shown in Figure :.6. Other results sho~ed similar asymptotic behavior of the curves indicating for Case, the expression for L lim is a good approximation. Above L,, T becomes quite indepen 1 1m dent of L and is reasonably equal to T.. a The problem of the stability of the effective column on elastic foundation taking the torsional weakening of the flange into consideration is finally reduced to the following: P cr T(l ~)P 1T~P e e.,., when BL 60 /P e < P cr T(O ;~L2)p when BL 2 /P e > Y( e e T, the torsional reduction factor is determined as follows: h if L > L l, - 1m 2.28 T T ( L) ( h ) ( L ) if L < L 1im L 1im h yo L lim. where

26 18 Yo = distance from the centroid of the equivalent column to its shear center h = distance from the tension flange to the centroid of the equivalent column For the case where the beams are braced at large distances, the following expression for P cr may be used: 2.30 Equation 2.28 for T is the expression further simplified from o Equation 2.23a, developed by the AS and the one in use in its Design Manual. l Equation 2.29 represents the linear interpolation T = LTa/L lim.

27 EXPERMENTAL CHAPTER 3 NVESTGATON 3.1 General The general theory of laterally unbraced compression flanges is quite involved as was discussed in the preceding chapter. n order to bear out the theory and simplifying assumptions, and to test the reliability and/or validity of the treatment of laterally unbraced compression flanges for diaphragm-braced beams, a series of tests was performed. The rationale behind this series of tests was to restrict variables to the minimum: hence the testing of simple spans and single bay assemblies. 3.2 General Procedure The experimental investigations conducted were to examine the ultimate load capacity together with the relevant parameters involved, of Z-section purlins assembled as roof systems with galvanized panels. The loading is to simulate uplift load due to wind on the roof system. Several purlin sections were made available by two manufacturers who also provided galvanized panels and their required fasteners. Two sets of tests were performed for each purlin-section. These are referred to as vacuum tests and beam tests. The details are described below. The choice of the Z-section purlins is essentially due to the common usage of this type of section as roof purlins in industrial-type metal buildings. ~9

28 Vacuum Tests A series of tests referred to as vacuum tests were carried out for each purlin section. Two twenty foot sections of the same purlin were assembled with galvanized roof panels to form the roof. This length was chosen to represent the portion of the purlins in the exterior span of a continuous purlin assembly. The distance between the exterior support and the first inflection point in the common case of twentyfive foot span purlins is about twenty feet. The purlins lie horizontal and parallel at five feet apart. The panels were screwed to the purlins using self-tapping screws for purlins already provided with prepunched holes. For purlins without prepunched holes, self-drilling screws were used. The screws were at one foot spacing. An overlay of polyethylene sheeting was provided between the purlins and the panels, and was taped to the floor before testing. A vacuum suction was then applied using a workshop vacuum cleaner. Two valves were provided to control the required vacuum suction. The applied pressure load was measured using a water manometer. Figure 3.1 shows the overall view of the purlin assembly, and Figure 3.2 gives the dimensional details. The panels used has the cross-sectional dimensions shown in Figure 3.6. t should be noted that the initial assembling of the roof assembly was done in the 'correct' position, i.e., the panels were on top of the purlins. The assembly was then inverted, the polyethylene sheeting taped to the floor, thus enabling a convenient

29 21 method of applying the uplift load. Reference to these tests are designated by the letter 'V' followed by a number signifying the sequence, e.g., test V3 means the third vacuum test done. With the exception of the first vacuum test (test V) which had rigid end supports, all the tests had simply supported ends. The simple supports were provided by placing rollers under the support -beams at both ends of the purlins to which they were connected to by using only one bolt not tightly bolted. The rigid end conditions for test V were obtained by attaching the purlin ends by means of two bolts to the end supports which were not free to rotate. The initial sweeps at midspan of the top web to flange junction of the purlins were measured relative to the same point at the purlin ends (see Figure 3.7). The strains and deflections under load were measured at midspan. The strains were measured using strain gages located mainly at the top flange region i.e., the compression flange. The horizontal and vertical displacements were measured by dial gages suitably located. The relative locations of the strain gages are as shown in Figure 3.9. All the tests were continued until failure occurred in one or both of the purlins. 3.4 Beam Tests A parallel part of the experimental program was a series of tests on similar Z-section purlins as in the vacuum tests referred to as the beam tests. Two twenty feet sections of the

30 22 same purlins were connected together along their bottom flanges by sixteen channel sections at one foot apart. arrangement provided a bracing system for the purlins. This At one-fifth points along the spans, a sixteen-inch small section was used instead of the channel sections. These were the locations of the applied load. The ends of the beam test assembly were simply supported with rollers. A four point loading system was applied to the bottom flanges parallel to the web. The loads were applied via the four small -sections connected to the bottom flanges. The test was done using a universal testing machine. Figure 3.3 gives an overall view of the beam test assembly under load. Figure 3.4 shows a schematic diagram of the assembly and some dimensions. As in the vacuum tests, the initial sweeps of the purlins at midspan were measured prior to testing (see Figure 3.8). Also, the strains and deflections were obtained at similar locations at the midspan. 3.5 Rotational Restraint Tests A series of tests were conducted to determine the rotational restraint provided by each purlin-panel system. For each purlin section, a three feet section was obtained and connected to a section of the roof panel with the screws as used in the vacuum test assembly. The procedure followed was that proposed by Haussler. 9 A schematic diagram of the assembly is shown in Figure An initial test was done according

31 23 t o a mo d 1 f' lcatlon. by Pe k" oz 11 0 f a procedure used by Celebi4 and used for similar purposes as this study. near identical results for the rotational factor, F, Both procedures gave in the initial tests. However, the Haussler method was preferred since it is simpler and was used in subsequent tests. The tests were continued until excessive rotation of the purlins and substantial buckling of the roof panels were observed. Care was taken to measure the gage and load direction heights at each loading as these differ substantially as the purlin rotations increase. Some measure of the rotational restraint on the purlins in the beam test set-up was needed. The F value for these tests would evidently be different from that of the vacuum tests. A two feet section of a purlin was taken. Two channel sections used for bracing in the beam tests were bolted at one end each to the purlin. Figure 3.11 shows the set-up used, which is a modification of the Haussler procedure used for the purlin-panel rotational restraint tests described above. The channels are rigid, hence the presence of the small -beams at one-fifth points along the actual beam test assembly should not alter the rotational restraint provided significantly. 3.6 Shear Rigidity Tests The shear rigidity of the roof panels was determined using a method called the centilevel shear test used by Pekoz,ll among others. Figure A schematic diagram of the assembly is shown in The specimens for the two tests done were the

32 24 two halves of the purlin-roof panel assembly of the vacuum test V3. The results of these tests are shown graphically in Figure Material Properties Three tensile coupons were prepared according to ASTM standards from lightly stressed regions of the failed purlin for each purlin type used in the vacuum tests. The average of the tensile yield stresses obtained are presented in Table Section Dimensions The purlin section dimensions were determined using a procedure that has been used in the metal building industry. This involves obtaining a portion from each purlin about eighteen inches long, and squaring one end reasonably flat. Next, a profile of the purlin was obtained by placing the flat end on a piece of tracing paper, and paint sprayed lightly around the perimeter of the section. The dimensions of the purlin were then conveniently measured from the image obtained. For the same purlin type, the dimensions are averaged and presented in Table Discussion of Test Results Test Results Under ideal circumstances, one would expect the purlin failure to be due to buckling in the compression region and in the vicinity of the midspan. The tests conducted showed

33 25 buckling in essentially three ways: (i) buckling at the compression flange-web junction at midspan or at the prepunched holes used for sag rods in an actual roof assembly, (ii) buckling at the web compression region at midspan or at the prepunched holds, and (iii) buckling at the lip-stiffener of the compression flange. These are shown in Figures 3.13 to 3.18, and a summary of the results is presented in Table 3.3. Details of the failures observed are as follows: Vacuum Tests: Test V: --Purlin type A. Failure occurred in one purlin by local buckling at 4.8 in. from the midspan where the prepunched holes were. The purlin ends were fixed, hence a high failure load obtained and the purlin maximum rotation was comparatively small (see Figure 3.13). Test V2: --Purlin type B. Local buckling occurred in one purlin at the hole location 1.6 in. from midspan. Yielding was observed as failure load was approached resulting in large lateral deflections of both purlins. The vertical deflection of the assembly was also observed to be large (see Figure 3.15). Test V3: --Purlin type D. Local buckling occurred in one purlin at the web and at midspan. t occurred after some observable yielding of the failed purlin. This test was one of two that showed the failure described, i.e., at the web only.

34 26 Also, from this test onwards care was taken to ensure that the purlins' holes are symmetrical Test V4: Test V5: Test V6: Test V7: about their midspan (see Figure 3.17). --Purlin type'c. Local buckling occurred at 6 in. from midspan at the location of prepunched holes of one purlin. No noticeable yielding was observed (see Figure 3.16). --Purlin type A. This was essentially a duplicate test for purlin A, except that the ends of the purlins were simple i.e., free to rotate. The failure occurred in one purlin by local buckling at the compression flange-web junction. The failure load was lower, and rotations and deflections larger than in test V. --Purlin type E. Self-drilling screws were used on this purlin type for panel connection. The failure occurred at midspan by flange lipstiffener failure of one purlin followed by the other. The stiffeners were twisted outwards until buckling occurred (see Figure 3.18). --Purlin type B. This was a duplicate of test V2 to verify the results obtained earlier. Failure occurred at the prepunched hole location by local buckling in the web compression region of one purlin.

35 27 Beam Tests Test B: Test B2: Test B3: Test B4: Test BS: --Purlin type A. Failure occurred by sudden local buckling of the compression flange-web region at the location of the prepunched holes of one purlin. This was S in. from the midspan of the purlins (see Figure 3.14). --Purlin type A. One of the two purlins used in this test was the purlin that did not fail fn test Bl. This purlin failed in this test in the same manner as in test Bl, 12 in. from the midspan. --Purlin type A. The failure load was lower. This is a duplicate of test Bl. Failure occurred in one purlin by local buckling as in test Bl, but at midspan. The failure load was nearly the same as in test Bl. --Purlin type D: Failure occurred by buckling of the flange lip-stiffener of one purlin. other purlin deflected considerably and was restrained by the test machine column. The t is envisaged that failure would have occurred in this purlin by local buckling of the compression flange-web region had not it been for the restraint described. (see Figure 3.17). --Purlin type B. The failure was violent Failure occurred in one purlin at midspan after large lateral deflections

36 28 Test B6: Test B7: indicating yield. Failure was of the local buckling of the compression flange-web-type. --Purlin type C. Failure occurred in one purlin at 6 in. from midspan at the prepunched hole location. The failure was as in test Bl. However, at failure, the other purlin reacted violently and showed failure in the lip-stiffener of the compression flange (see Figure 3.16). --Purlin type E. The failure occurred in one purlin by buckling of the compression flange lip-stiffener. Small lateral deflections were observed as was the case in test V6 for similar type purlin (see Figure 3.18) Discussion of Vacuum Test Results The failures in the tests conducted occurred mainly in the compression flange-web region of one purlin. With the exception of test V3 and V7 where the local buckling was observed to be at the webs only, it was difficult to observe whether the local buckle appeared initially in the flange or the web as it happened suddenly in most cases. For tests V2, V3 and V7, the purlins used were of low flange-width to thickness (wit) ratios (purlin types Band D with wit = 24.3 and 22.3, respectively). The approaching failures were easily anticipated by the large lateral deflections observed with each load increment,

37 29 indicating yield. n general at failure, the purlins deflected laterally in a continuous manner at constant load until local buckling occurred at the location of high compression stress. The purlins of high wit ratios, namely purlin types A, C and E all failed by sudden local buckling in the compression flange-web region in the case of purlin types A and C, or at the lip-stiffener of the compression flange in the case of purlin type E. t is interesting to note the failure of purlin type E. The initial sweep (see Figs. 3.7 and 3.8) of this purlin type tended to be negative as defined by Figure 4.2 Hence, the twisting outwards of the lip-stiffener of the compression flange began almost immediately upon loading. t is envisaged that a higher load could be obtained if the initial sweep had a small positive value. For the other purlin types, the tests did indicate a tendency to buckle at the prep~nched holes. The absence of these holes should give higher ultimate load capacities for these purlins Discussion of Beam Test Results The failure modes in the beam tests conducted are generally of the same type as those in the vacuum tests. For the various purlin types, the behavior at failure was the same. The beam tests thus model the behavior in the vacuum tests adequately. Considering the two types of tests as a whole it can be observed that the purlins of low wit ratios tended to buckle locally at midspan, whereas those of higher wit ratios tended to do so at the location of the prepunched holes.

38 CHAPTER 4 ANALYSS OF RESULTS 4.1 General The analysis of diaphragm-braced purlins is a complex problem. Among other procedures for analysis, that of the AS Cold-Formed Steel Design Manuall-Part, Section 3, was tried. The basis for this procedure is the study by Douty6 which has been described in some detail in Chapter 2. The studies presented by Desmond S and yu 13 will also be utilized to assist in understanding the analytical and design problem and arrive at suitable design recommendations. An available computer program based on analytical studies by Celebi 4 and modified by Pekoz ll was also used to obtain theoretical values to compare the test data with. 4.2 Background for Evaluation of Results AS Design Manual (Part, Section 3) Approach (Douty Approach) Part, Section 3 of the American ron and Steel nstitute (AS) Cold-Formed Steel Design Manual l (henceforth referred to as the Douty approach), is the basis used for analyzing the quantitative information obtained from the experimental program of this study. The Douty approach requires the following: 1. The location of the neutral axis is determined for the purlin section. The "equivalent column" is defined as the portion of the beam from the extreme compression fiber to a 30

39 31 level which is (3C c - C t )/12C c d distance from the extreme compression fiber. Here, C c and C are the distances from the t neutral axis to the extreme compression and tension fibers respectively, and d is the depth of the purlin section. 2. The shear center is located for the distance y o measured parallel to the web from it to the centroid of the equivalent column (see Figure 4.1). Approximation is allowed, for example, if the flanges of the channel-shaped compression portion of the section are of unequal width, one can take w as the mean of the two flange widths. More exact methods of analysis can be used to locate the shear center. 3. The spring constant, a, is then determined. This is done by taking 1 inch long portion of the purlin, apply a force of kip perpendicular to the web at the level of the column centroid, and compute the corresponding lateral deflection D of that centroid. follows: a = O.OOl/D The spring constant is then 4. The torsional reduction factor, To' is computed as T = o h + h 3.4yo where h is the distance from the tension flange to the centroid of the equivalent column, and Yo is as defined in 2. S. For the flange braced at less than two points, (which is the case for this study), the critical load of the equivalent column, P cr is computed as follows: P = T /4BE cr 0

40 32 where is the moment of inertia of the equivalent column about its y axis parallel to the web, e is as defined in 3, and E is the modulus of elasticity. f the flange is laterally braced at two or more points, P cr is computed as in p. 19 of Part of Reference The slenderness ratio of the equivalent column is then determined as follows: ft (KrL) eq = k ";X cr c where k is an experimental correction factor for the post-buckling strength of the section and equals 1/1.1, and A c is the cross-sectional area of the equivalent column. With E = ksi, the equation reduces to: 7. The axial stress F al, at the level of the centroid of the equivalent column, corresponding to (KL/r)eq' is computed from the equations in paragraph (a) of Section of Reference 1 (using Q = 1 and K = 1). without the factor of safety, are: These equations, F KL < fi!}'te or - -,.;-- r - r y

41 33 2 F = it E al (KL/r) 2 A note about the above formulas is in order. The value of ;!2iT 2 E/F y is the limiting KL/r ratio corresponding to a stress equal to F y /2 in flexural column buckling. When the KL/r ratio is greater than this limiting ratio, the column is assumed to be governed by elastic buckling, and when the KL/r ratio is smaller than this limiting ratio, the column is to be governed by inelastic buckling. factor of safety of 23/12 is used. n the actual design formulas, the 8. The compression bending stress in the extreme compression fiber, F b2, the axial stress F al : C F b2 = (r) F al c is then computed by extrapolating linearly where C is the distance from the neutral axis of the beam c to the extreme compression fiber, and Y c is the distance from the neutral axis of the beam to the centroid of the equivalent column. n the Design Manual, F b2 is multiplied by a factor of 1.15 being the ratio of the factor of safety used for column buckling (23/12) to the factor of safety used for beam yielding (5/3), F al having the factor of safety of (23/12) to it beforehand. applied

42 Discussion of the Douty Approach n the second step of the Douty APproach, the computation of Yo' the distance from the centroid of the compression area to the shear center, parallel to the web, is easily established for a channel-shaped configuration with equal flanges. A reasonable approximation can be made for a channel with unequal flanges by taking the flange width as the mean of the two unequal flanges. For a channel with one flange angled, the required shear center distance is computed more accurately by a method as presented in Appendix A. t is observed that the computed values of Yo by this method is smaller as compared to the values obtained by the approximate method suggested by the Douty Approach. For the same section, this leads to a higher computed stress being obtained. n the third step of the procedure, a spring constant, S, is computed. This spring constant represents the rotational restraint provided by the section when Subjected to an applied moment. n the procedure for computing S suggested by the Douty approach, a one inch long portion of the member is isolated, a force of kip is applied Perpendicular to the web at the level of the column centroid, the corresponding lateral deflection D of that centroid is computed, S is then equal to O.OOl/D. This study involves purlins braced continuously by panels. There is a restraining action by the panel on the rotation of the purlin section, hence the value of S must reflect this action. An analytical procedure would be too

43 35 complex for ease of computation. Two experimental procedures are available for a reasonably accurate determination of the rotational restraint factor, F, from which S can be easily computed for sections such as the Z-sections used in this study. S = F/d 2 r where d r is the distance from the centroid of the equivalent column to the axis of rotation, which for the Z-section is the web-tension flange corner. The procedures as used by Pekoz and proposed by Haussler 9 were discussed in Section 3.5. The significance of using different values of F for a particular cross-section is discussed further in Section The concept of effective width of a plate element under compressive stress is well established in cold-formed steel design. Winter's commentary on the AS Cold-Formed Steel Design Manual (Part of Reference 1) gives a summary of this concept as currently used by the AS. This concept is of great significance in the procedure discussed since the ultimate load capacity of a purlin depends on the sectional modulus used. Other computations involve the determination of the centroid of the compression area (equivalent column) and its moment of inertia. These geometrical parameters depend on the amount of the compression flange considered. n general, the Douty approach is currently applied assuming the compression flange as fully effective. However, in the evaluation of the test results

44 36 in Section 4.3, the use of the effective section properties were also tried. The work of Desmond S was used in this regard since it uses the concept of effective width for a stiffened as well as partially stiffened and unstiffened plate elements Adequacy of Compression Elements The material discussed in this section is drawn from the study by Desmond S on the behavior and strength of thin walled compression elements with longitudinal stiffeners. Desmond presented the stiffener requirements and design procedures for predicting effective widths of edge and intermediately stiffened elements. He adhered to existing design procedures of the AS Design Manual l as far as possible. n his design method, the flange stiffened by an edge stiffener is examined, depending on its (wit) ratio and the yield stress, whether it is fully effective as an unstiffened element, fully effective when adequately stiffened or it is in the post-buckling range. The last two categories require adequate stiffening for which formulas are provided. The edge stiffeners are then examined for their adequacy. For an adequately stiffened flange, the flange and stiffener effective widths are then computed. For a partially stiffened flange, its effective width and the reduced area of the partial stiffener are determined. From the reduced area of the partial stiffener, the reduced length is obtained. The reduced length is treated like an effective width for computations of section properties. All the effective width equations are drawn from Winter'sl equivalent width relationship or modifications of it.

45 37 Essentially, Desmond presented modified values of the buckling stress coefficient. A summary of Desmond's design method is presented in Appendix B. 4.3 Evaluation of Results Test Ultimate Loads The ultimate loads for the vacuum tests and the beam tests are presented in Table 3.3. A uniformly distributed load was applied in the vacuum tests. The maximum moment occurs at midspan and is equal to w1 2 /8 where w is the uniformly applied load per linear foot of purlin, and 1 is the purlin span. For a section modulus 5 of a purlin, W v = 805/12, where o is the stress in the extreme fibers and W is the distributed v load corresponding to stress 0. A four point loading is applied in the beam test (see Figure 3.4). By considering the maximum moment at midspan, the load per linear foot is w b = (20/3)05/1 2. For the situation where the purlins in both tests have the same failure stress, wv/w b = 1.2. From an inspection of the ratios of the actual test values, the theoretical ratio does not hold, the mean being However, wb/w v has a mean value of A possible explanation is that in the actual tests, the purlins of the same section do not reach the same failure stress in the vacuum as well as the beam tests, as assumed above. t is expected that since the rotational restraint factors, F, for the same purlin section in the two set-ups, vacuum and beam, are different, (the latter is expected to be higher), the ultimate stresses, hence ultimate loads are predictably no longer in the

46 38 ratio of 1.2. Further, the purlins were not subjected to pure flexural action Test Ultimate Stresses The ultimate stresses (computed from the last recorded strains before failure occurred) reached in the vacuum and beam tests are presented in Table 4.1. Load-strain curves for the five purlin types tested are presented in Figures 4.3 to The locations of the strains recorded are indicated by numbers corresponding to those in Figure 3.9. All the tests indicated the highest stresses (corresponding to the highest strains) occurred at locations 4 and 5 on one purlin, or the corresponding locations 9 and 10 on the other purlin in the pair, depending on which purlin failed. The exception was for tests on purlin type E, where the failures were due to local buckling of the lip-stiffener of the compression flange. Both purlins in test V6 showed high stresses at similar locations 2 and 7, and 5 and 10 (at top of web). n test B7, one purlin showed highest stress at location 1 (at lip-stiffener) on one purlin and at location 10 (at web) on the other purlin. t is interesting to note that the initial sweeps of the purlins in test V6 are both negative (see Figure 3.7), whereas that of B7 are both equal and opposite. n the vacuum tests, the failures occurred at stresses varying from 45.3 to 87.3 percent of yield stress (see Table 4.1). One test of purlin type B failed at yield, another at 79.2 percent of yield stress. Generally, purlin types with high flange width to thickness ratios failed at lower stresses

47 39 (average of 62.2 percent of yield stress) than that of low ratios, i.e., thicker purlins (average of 83.2 percent of yield stress). The failures in these tests than are governed by buckling of the plate elements rather than by yielding, as can be expected. The load-stress curves of the highest stressed location for each purlin type in the vacuum tests were compared with the curves obtained for the same location using an available computer program (due to Celebi 4 and Pekoz ll ). These curves are shown in Figures 4.13 to With the exception of curves for purlin type B, all the curves show fair correspondence, less so at higher loads. The test stresses were computed directly by multiplying the strains with the modulus of elasticity (29500 ksi). These would then be comparable directly with the computer program results where elastic behavior is assumed for any load Test Ultimate Rotations The maximum rotations computed from deflection measurements are presented in Table 4.2. The load rotation curves for the two types of tests are presented in Figures 4.18 and The behavior of purlin type E in the vacuum test, as have been pointed out in this report previously, is somewhat different from the other purlin types. Due to the compression area twisting outwards (i.e. in the negative direction according to Figure 4.2), which led to the failure of the lip-stiffener, it did not show the torsional behavior exhibited by the other purlin types. The load-rotation curve is linear up to failure,

48 40 with the maximum rotation only of the order of one quarter of the other purlin types. The maximum rotations, with the exception of that for purlin type E for the vacuum tests and purlin types D and E for the beam tests, are fairly close with one another. mean is radians with a standard deviation of t has been suggested that a failure criteria based on ultimate rotations could be formulated Rotational Restraint Factor, F The An important factor in considering the ultimate strength of the purlins is the rotational restraint the roof panels provide when the whole assembly is loaded. The degree of rotational restraint is dependent to a certain degree on the cross-sectional dimensions of the purlins, the rigidity of the panels to which they are connected and the nature of the connection. vacuum and beam tests. The last two factors were different for the These have been described in the assembly details for the two types of tests in Chapter 3, and is further discussed below. Three initial tests to evaluate the rotational restraint factors F, were done according to the method used by Pekoz,ll all the remaining twelve tests were conducted using the pro- 9 cedure proposed by Haussler (see Section 3.5). The results of the tests (1) with the purlins diaphragm-braced and (2) the purlins braced with sixteen inch length channel sections are presented in Figures 4.20 to The rotational deformation of the purlin web with respect to its bottom (tension) with

49 41 flange was also computed from the deflections measured at a point near the mid-point of the web, parallel to the bottom flange. The ratios of these rotations to the total rotations were computed and are presented in Table 4.3. The rotational restraint factor, F, was computed for each purlin and test type by obtaining the moment M corresponding to the maximum large-scale test rotation. by the maximum test rotation. This was done since the momentrotation curve is nonlinear. Mis then divided The value of F increases with increasing rotation. The F values are presented in Table 4.2. t is generally observed that the F value is higher for a purlin section that has a low web depth to thickness ratio (Hit). Figure This is indicated in a plot of Hit vs. F shown in Also from Table 4.3, it is observed that generally, purlin types of high Hit ratios suffer more cross-sectional rotational deformation than those of lower Hit ratios. Purlin type E is consistently enigmatic in its behavior, even in this case since in both the diaphragm-braced and channel-braced F tests, its web cross-sectional rotational deformations (per total rotations) are higher although its Hit ratio can be considered as intermediate between those of Band D, and A and C Shear Rigidity of Panels The knowledge of the shear rigidity of the panels is required for use in the computer program computations. shear rigidity, Q, computed from Figure 4.24 is 30 kips, calculated according to a method given by Apparao and Errera. 2 The

50 42 This value is somewhat lower than those obtained by Pekoz. ll There are intentional differences in the framing of the panels in the tests done in the two cases (see Figure 68 of Reference 11 and Figure 3.12 of this report) nitial Sweeps of Compression Flanges The initial sweeps of the compression flange-web junction of the purlins were measured relative to a straight line joining the two ends (for the same locations) at the supports. The values obtained are presented in Figures 3.7 and 3.8 for the vacuum and beam tests respectively. The initial sweep seems significant in predicting which purlin out of the two in the test assembly would fail and what kind of failure would occur, namely local buckling in the vicinity of the compression flangeweb area or local buckling at the lip-stiffener of the compression flange. The purlin that had the larger initial sweep of the two generally tended to fail first. Local buckling at the web-flange junction occurred when the initial sweep was positive (see Figure 4.2 for deflection sign convention used). This type of failure occurred in most types of purlins tested and in these purlins the initial sweep was in the negative direction. This was the case for purlin type E in both the vacuum and beam tests. t must be added that comparing with the other purlin type whose Hit ratio is fairly close, the ultimate load obtained for purlin type E was low. t is envisaged that besides the nature of the initial sweep discussed above, purlin type E has a comparatively longer flange width and shorter lip-stiffener which probably contributed to the lower ultimate strength reached.

51 Ultimate Loads General The tested purlin sections, with measured dimensions as in Table 3.2, were analyzed for ultimate loads using various relevant sections of the current AS Specification for the Design of Cold-Formed Structural Members (Part of Reference 1), henceforth referred to as the Specification, as well as the Douty approach (Part, Section 3 of Reference 1). Specifically, the effective widths of flanges were used for computation of the section properties necessary for determining ultimate loads. The adequacy of the lip-stiffeners were checked. The procedure was repeated using the findings of Desmond regarding flange and stiffener adequacy Computations Based on Full Widths of Flanges The procedure outlined in Section (the Douty approach) was used in computing the ultimate stress at the extreme fibers under compression. From consideration of the loading system used, uniform loading for the vacuum tests and a four point loading for the beam tests, the ultimate load was computed. Using basic mechanics, the load per linear foot of purlin, q in the vacuum tests is: q = 8crS/L 2 where cr = ultimate stress S = section modulus of purlin L = span length For the loading in the beam test set-up, the total load, W, is:

52 44 The ultimate loads were computed based on the full widths of the purlin dimensions for determination of section properties. This assumes that particularly the compression flange is fully effective. The computations were done on the basis of sharp corners at the web-flange and flange-stiffener junctions. From Table 3.2, it is observed that the corner radius to thickness ratios are generally of the order of four or greater. Hence, this approximation relieves computations of the corners. The computed ultimate loads were compared with the ultimate test loads for each pur1in type. The results are tabulated in Tables 4.6 and 4.7 (Column a) for the vacuum tests and beam tests respectively. These computations used the tensile coupon test yield str~ss as ultimate stress. Also, the rotational restraint factor, F, has different values for each purlin type. Further, for each purlin type, the F values are different for the case when it is diaphragm braced and when it is rigidly braced as in the beam test setup. A similar series of computations were done using F bw given below, as ultimate stress: F bw = [ (hit) JF';] F y The above equation is proposed by yu l3 for the maximum compressive stress in the web for beams with unstiffened compression flanges. For the pur1in sections used, F bw is presented in

53 45 Table (Column b). The load ratios are presented in Tables 4.6 and Computations Based on Effective Widths (ArS) The relevant sections of the Specification used here are Section for effective width determination: where wit = Flanges are fully effective up to (w/t)l 1m For flanges with wit larger than (w/t)l 1m b = b = t 326 [1 _ 71.3 ] (wit) T flat-width ratio effective design width, inches f = actual stress in the compression element = 2211 t computed on the basis of the effective design width, ksi. and Section for edge stiffener requirements. The minimum moment of inertia:. = 1.834t 4 /(w/t)2-4000lf y but not less m1n than 9.2t 4 where wit = minimum allowable moment of inertia of stiffener about its own centroidal axis parallel to the. 4 stiffened element, 1n. Using the above, the effective widths were computed using the yield stress, F, as the ultimate stress. n computing y, the fact that the lip-stiffeners in the test purlins were min angled at less than right angles with the flange was taken into account. The results of these computations are presented in

54 46 Table 4.8. The computed values of adequate and actual moments of inertia show that using the full flange width, only purlin type C is adequately stiffened. The others were as much as 56 percent less than adequate. Computations showed that increasing the lip-stiffener angle would increase the required moment of inertia. For purlin type E however, increasing the lip angle to 90 degrees would not help. A longer lip-stiffener is required to meet the minimum stiffener requirements. Using the flat flange width as a basis for computing the minimum stiffener requirement showed that all the purlin types except E are adequate. t has been shown in Section that since the corner radius to thickness ratios are generally larger than 4, computations based on sharp corners are reasonable. Hence, the total widths were preferred in the computations. The Specification states that in order that a flat compression element may be considered a stiffened compression element, the stiffeners must have the minimum moment of inertia as given above. This being the case, one can treat all the purlin types tested, except C, as being unstiffened. The Specification does not provide for obtaining the effective width of an unstiffened element. This will be considered in Section Computations Based on Desmond's Flange and Stiffener Adequacy R equ1rements 5 Desmond's study was briefly discussed in Section and his procedure for the determination of flange and stiffener adequacy and formulas for effective widths are presented in

55 47 Appendix B. Using this procedure then, effective widths of the compression flanges, and effective widths of adequate lip stiffeners or reduced length of partial stiffeners as the case may be, were computed. Both the total widths and flat widths of the compression flanges and lip-stiffeners were used as the bases for the computations. The computations were done using F y (the tensile coupon test yield stress) as ultimate stresses. The computed widths are presented in Table 4.9. These computed widths were used for the compression flange area in computing the section properties required in the Douty approach for determining ultimate stresses in laterally unbraced compression flanges. The ultimate loads were then obtained as in the previous computations, and compared with the test ultimate loads. The ratios of the computed and ultimate loads were obtained for the four cases as given in Tables 4.6 and 4.7 (Columns c, d,e and f). Desmond also gave provisions for the case when the compression element is unstiffened (Refer Appendix B). To obtain a lower bound for the computed strength the width of the compression flange was also taken as the total of the actual length of the flange and the lip-stiffener length. Equation B.18 of Appendix B was then used to obtain the flange effective widths for the two cases using F and F y bw as ultimate stresses. These widths are given in Table 4.7. t is interesting to note that the computed effective widths vary from 28.3 to 46.7 percent of the actual widths considered which are rather small.

56 48 The ultimate loads were obtained as before and compared with the test loads. These load ratios are presented in columns (g) and (h) of Tables 4.6 and 4.7. With these computations, the series of computed ultimate loads for the five tested purlin types are completed. 4.5 Discussion of Analysis The analyses undertaken in the preceding sections were done to establish a reliable failure criteria for cold-formed steel Z-purlins. Although the analyses were done based on experimental data that were obtained under uplift load conditions, any prediction of ultimate loads should be generally applicable due to the point symmetric nature of the Z section. Any flexural action of the purlins would introduce torsional weakening, hence reduce ultimate loads computed simply on the basis of only flexural beam action. The ultimate stresses in the diaphragm-braced purl ins at failure were below their yield stresses. The failures were due to local buckling of the plate elements at the compression flange-web junction or at the lip-stiffener of the compression flange, rather than by yielding. n the beam tests, the strains measured indicated that yielding occurred for purlin types B, C and D, although local buckling in the compression flange-web junction did occur in most cases. Referring to Table 4.6, the mean, standard deviation and standard deviation/mean of the test load/computed load ratios were computed for each analysis type for the vacuum tests.

57 49 From column (a) of this table, purlin types A and B (depth 9.45 and 9.46 inches respectively) showed excellent correlation between observed and computed ultimate loads, allowing for slight conservatism, when full flange widths were used. load ratios are low however, for purlin types C and D and lowest for purlin type E. is not a satisfactory correlation. The Overall, a mean of 0.88 was obtained which Column (b) of the same table shows a slight improvement in the mean value, but still unsatisfactory. The use of a lower ultimate stress, F bw (the maximum web stress - see Table 4.4), which underestimates the strength, does not help when full flange width was used. An improved correlation between observed and computed loads was obtained when effective flange widths and effective widths of the lip-stiffeners, or reduced lengths of partial stiffeners as the case may be, were used in the computations. Analysis type (d) shows an overall mean of This analysis used the maximum web stress, F bw ' as the ultimate stress. gnoring the load ratio for purlin type E gives a mean of 1.05 for analysis type (c) which is satisfactory. Excluding results for purlin type E could probably be justified by the fact that its observed ultimate load compared with the computed load seems consistently small for the first six analysis types and by other considerations discussed variously in the preceding sections of this chapter. Analysis types (e) and (f) used effective widths computed on the basis of flat flange and stiffener widths, and using the yield stress, F and P respectively for ultimate stresses. y b w

58 so Slight improvements over analysis types (a) and (b) are indicated. Analysis types (g) and (h) used the effective widths of unstiffened compression flanges (which they were shown to be in Section 4.4.3). Both analyses are evidently very conservative to be of design use. The concept of partial stiffeners proposed by Desmond S would be more realistic for inadequately stiffened flanges. Looking at the analysis for the beam test ultimate loads presented in Table 4.7, one can say that analysis type (f) shows good correlation between observed and computed ultimate loads. This analysis used effective widths computed from flat flange and stiffener widths and F bw as the ultimate stress. However, again ignoring the load ratio for purlin type E, analysis type (c) gives a mean of 1.03 for the load ratios, which is good. nherent in all the analysis types for both vacuum and beam tests is the use of a unique rotational restraint factor, F, for each purlin type. Besides using an experimental procedure to determine F, a simple design method need yet to be established. 4.6 Summary The analyses showed that the Douty approach as given 1n the current AS Design Manual l (Part, Section 3) on the design of laterally unbraced compression flanges is inadequate for the determination of ultimate strength of cold-formed steel Z-purlins. The use of effective widths for compression

59 51 flanges and effective widths of adequate stiffeners or reduced length of partial stiffeners as the case may be, as proposed by Desmond 5 gave a good correlation between observed and computed ultimate loads. Using the maximum web stress, F bw ' of unstiffened compression flange as proposed by yu 13 provided slightly more conservative results. The value of the rotational restraint factor, F, to be used in the analyses is of significant importance.

60 CHAPTER 5 CONCLUSON 5.1 Summary of Results The research described herein studied the ultimate strength of braced cold-formed steel Z-purlins subjected to uplift loads. An experimental investigation was undertaken to obtain quantitative information. Five types of cold-formed steel Z purlin were used in large-scale tests of two kinds: and beam tests. width to thickness ratios. vacuum These purlin types have different flange The tests were undertaken to determine the ultimate load capacity of the purlins. Experimental values of the rotational factors, F, were determined at least once for each purlin and test type. The information obtained from the tests conducted and the analyses done on them were reported in Chapter 3 and 4 respectively. Chapter 2 detailed a Cornell University study undertaken by Douty.6 The experimental results were analysed using the AS (or Douty's) approach given in its Design Manual l (Part, Section 3) and Desmond'sS design method for edge-stiffened thin-walled compression elements. The AS approach was found to be generally unsatisfactory in predicting the ultimate strength of the Z-purlins used. The analyses showed that the compression flanges and their lip-stiffeners cannot be treated as fully effective in most cases, especially for purlin types that have high flange width to thickness ratios. The AS 52

61 S3 approach as it stands lead to unconservative results. When used in conjunction with Desmond's design method however, which uses the concept of effective plate widths, the AS approach was found to be able to predict ultimate strengths reasonably well. A more conservative result could be obtained by using Yu's maximum web stress, based on an unstiffened compression flange, as the ultimate stress in the design procedure given in the AS Specification. 5.2 Recommendations On the basis of the experimental results obtained and the analyses done through this research project, it is possible to recommend modifications to the current AS Design Manual,l Part, Section 3, which deals with the design of laterally unbraced compression flanges.insofar as it is used to predict ultimate strengths of cold-formed steel Z-purlins. The AS Design Manual Part, Section 3 can be utilized to determine the ultimate strength of Z-purlins, with the proviso that the compression flange and lip-stiffener be checked for their effectiveness by Desmond's design method as presented in Appendix B. The effective width of the compression flange and the effective width of the lip-stiffener or the reduced length of the partial stiffener, as the case may be, should be used. For a reasonably conservative prediction of ultimate strength, the maximum web stress as proposed by Yu l3 could be used as the ultimate stress instead of the yield stress.

62 54 known, Further, the rotational restraint factor, F, needs to be or at least a reasonably close approximation of it. Currently, the suggested method is by a simple test such as the method proposed by Haussler. 9 A convenient design procedure to obtain F is being studied at Cornell University. 5.3 Suggestions for Future Work This study is limited to the determination of ultimate strength of cold-formed Z-purlins. The use of channel-section purlins is also common in metal building construction for similar applications as the Z-purlins. Hence, besides further confirmatory tests on the applicability of Desmond's design method in determining effective widths for use in the AS Design Manual, Part, Section 3, the ultimate strength of channel-section purlins under uplift loads need to be looked into. Another important area to be looked into is a design procedure to determine the rotational restraint factor, F. empirical relationship between web depth to thickness ratio, yield stress, and F seems reasonable, should further quantitative information be available from extensive testing to justify it. An

63 APPENDX A LOCATON OF SHEAR CENTER FOR EQUVALENT COLUMN For the purpose of the computations detailed in Chapter 4, it is necessary to obtain the distance y, the vertical o distance from the centroid of the equivalent column to the sh~ar center. t is not necessary to know the exact location of the shear center. Referring to Figure A., let the shear center (S.C.) be as indicated, distance y v centerline. from the flange Applying a force P v as indicated on the shear center parallel to the flange, no twisting of the equivalent column could occur. Considering this condition, an attempt is made to obtain a good approximation of the shear center location. The variation of the shear flow along the lip-stiffener is taken to be linear as shown. This would be true for a regular channel section, but since the stiffener length for this case is normally short compared to the flange width, this would be a reasonable approximation. Using the usual notations, the maximum shear flow i~ stiffener is: V(st)(t + ~ cosa) ~= yy where yy moment of inertia of the lip stiffener about axis y-y the 55

64 56 Total shear force = Vs 2 t(l + 2 yy s coscx.) 2" Moment of shear force about 0, M 0 Vs 2 t(l + 2" s cosa)(l + m)sincx. M = 0 2 yy Moment of applied force P y about 0, Mp.. y M p y = pyyy For no twisting: Since py = V and with b = l + m Yy = s2t (l + ~ coscx.)bsincx. 2 yy The location of the shear center above the centroid is then: Yo = YNA + Yy

65 APPENDX B DESGN METHOD FOR EDGE STFFENED ELEMENT ntroduction The following design method for an edge stiffened element is taken from Reference 5. This design method is part of a complete design method proposed for stiffened elements which include intermediately stiffened elements. The stiffener requirements and design procedures for predicting effective widths are presented. Notation The following symbolism and definitions pertain to the typical edge stiffened elements shown in Figure B.1 and will be used in the subsequent design recommendations. (wit) = 2211 cry B.1 a. (w/t)a = (kw)u.s. Elcr y B.2 in which (k ) is determined by rotational w u.s. analysis per Figure of Reference 16. f rotational restraint at supported edge is neglected, then (k ) = w u.s. and (w/t)a = cry B.3 s = effective moment of inertia of edge stiffener about 57

66 58 its own centroidal axis parallel to the stiffened. 4 e1ement, n. f the stiffener is a straight lip then B.4 where B.5 in which r is the inside radius at the corner of the stiffener and flange, and from Equation (d/t)eff =.95/. 425 E (1. -.~J~/.425 E) B.6 0y. 0y when k d is taken as Also, if the straight lip stiffener is at an angle to the flange, d eff is determined from the above equation, but s is calculated by 3 D eff t 2 s = cos e B.7 12 where e is defined in Figure 6.lb. (s)adequate = Required minimum centroidal moment of and inertia of stiffener necessary to adequately support the flange. Stiffener moment of inertia is taken about its own centroidal axis parallel to the stiffened. 4 e1ement, ln. w = flat width of edge stiffened flange, in.

67 59 d = flat width of straight lip edge stiffener, in. k d = buckling coefficient for straight lip stiffener k = buckling coefficient for edge stiffened flange w 0 = yield stress, ksi y E = Young's modulus, ksi Edge Stiffener Requirements The required minimum stiffener rigidities, (s) adequate, necessary to adequately support the edge stiffened flange are as follows: --For (wit) < (w/t)13; fully effective as an unstiffened (s)adequate = 0 element - - For (w/t)13 2 (wit) < (wit) a.; fully effective range when adequately stiffened B.S f rotational restraint is neglected at supported ege such that (w/t)a. and (w/t)13 are defined per Equations 5.4.3a and 5.4.4a in Section 6.1.1, then 3 [(wit) - ( y) ] [(2211 ~) = 36.1 x 10-6 [(w/t).;a; ]3 --For (wit) > (w/t)a.; post-buckling range

68 60 From Figure 5.3.3, Stiffener Requirement V is given by Substituting Equation 5.4.3a, B.lO etermination of Effective Widths and Areas B.ll -For s ~ (s)adequate; Adequately Stiffened Element Effective Width of Flange is given by (wit) eff = 0.95 E(k ) w a.s. (1. _.209 cry WTt f D w < 0.25 or if stiffener other than a straight s - lip (such as L-shaped stiffener in Figure 6.lc) f D w > 0.25 then s (k ) -5 D w + w a.s. - s 5.25 where D is the unstiffened flat width of the s stiffener plus the corner radius. Effective Area of Adequate Edge Stiffener f straight lip stiffener B.13 (A ) = d eff t s eff where (d/t)eff.95 Jk:yE (1. - ~n/\e) B.14

69 61 --For 0 in which k d - f other than straight lip and if for none of the stiffener's component elements wit> (w/t)l" 1m then (As)eff = unreduced cross-sectional area of stiffener < s < (s)adequate; Partially Stiffened Element Effective Width of Flange is given by (wit) eff =0.95 B.15 where in which (kw)a.s. is defined above for the adequate stiffener and (k ) and is defined in the plate buckling coefficient w u.s. if the plate element were stiffened and if wit < (wit) CL n = 2 B.16 wit> (w/t)cl n = 3 Reduced Area of the Partial Stiffener is given by (AS)p.S. = (As)eff s/(s)adequate B.17 where (As)ef is defined above for the adequate edge stiffener.

70 62 --For s = 0; Unstiffened Element Effective Width of Unstiffened Flange is given by (wit) eff =0.95 E(k ) w u.s.) B.18 cry where (k ) = w u.s. unless determined by rational analysis per Figure of Reference 16.

71 REFERENCES American ron and Steel nstitute, Cold-Formed Steel Design Manual, Washington, D.C., Apparao, T.V.S.R. and Errera, S.J., "Design Recommendations for Diaphragm-Braced Beams, Columns and Wall Studs," Report No. 332, Department of Structural Engineering, Cornell University, thaca, N.Y., Bleich, F., Buckling Stren~th of Metal Structures, McGraw-Hill, New York, 195. Celebi, N., "Diaphragm Braced Channel and Z-Section Beams," Report No. 344, Department of Structural Engineering, Cornell University, thaca, N.Y., Desmond, T.P., "The Behavior and Strength of Thin- Walled Compression Elements with Longitudinal Stiffeners," Report No. 369, Department of Structural Engineering, Cornell University, thaca, N.Y., Douty, R.T., "A Design Approach to the Strength of Laterally Unbraced Compression Flanges," Bulletin No. 37, Cornell University Engineering Experiment Station, thaca, N.Y., Ellifritt, D., Private Communication. Haussler, R.W., "Strength of Elastically Stabilized Beams," Journal of Structural Division, ASCE Proceedings, Vol. 90, No. ST3, June Haussler, R.W., Private Communication. Kalyanaraman, V., "Performance of Unstiffened Compression Elements," Research Report No. 362, Department of Structu Engineering, Cornell University, thaca, N.Y., Pekoz, T., "Continuous Purlin Tests," Department of Structural Engineering, Cornell University, thaca, N.Y., Winter, G., "Lateral Bracing of Columns and Beams," Transactions ASCE, Vol. 125, Part, Paper No. 3044, Yu, Wei-Wen, Private Communication. Yu, Wei-Wen, Cold-Formed Steel Structures, McGraw-Hill, New York,

72 64 TABLES

73 65 TABLE 3.1 MATERAL PROPERTES (Tensile) Purlin Yield Ultimate Percent Type Stress (ksi) Stress (ksi) Elongation A B C D E

74 TABLE 3.2 AVERAGE PURLN DMENSONS(l) PURLN H b t w t St d t <P t Rt/t rt/t t TYPE (in) (in) (in) (in) (in) (degrees) (in) A B C D E PURLN bb w b sb db <Pb Rb/t rb/t 0\ TYPE 0\ (in) (in) (in) (in) (degrees) A B C D E (l)dimensions as in Figure 3.5

75 TABLE 3.3 SUMMARY OF TEST RESULTS TEST PURLN NOM. NOM. FAL LOCATON OF LOCAL BUCKLE (1) TYPE DEPTH THCK LOAD(2) (N) (N) (LBS/FT) AT A DST. OF BUCKLE HOLE(3) TO MDSPAN (N) COMMENTS (4) V A 9-1/ Y 4.8 (9) V5 A 9-1/ N m. s. B1 A 9-1/ Y 15 B2 A 9-1/ (10) B3 A 9-1/ N m. s. V2 B 9-1/ Y 1.6 (5) V7 B 9-1/ Y 6 B5 B 9-1/ N m. s. V4 C Y 6 (6) B6 C Y 6 V3 D N m. s. B4 D N m. s. (7) V6 E N m. s. (8) B7 E N m. s. (8) (1) (2) V designates vacuum - B designates beam test n the beam test, failure load is given as the total load on the span divided by the span length. 0\ --..J

76 TABLE 3.3 (continued) (3) Y-Yes; N-No. (4) Unless otherwise noted, local buckle occurred only in one purlin and in the web and the flange. (5) Yielding accompanied by large deflections. (6) ndicated buckling was in the web and the flange of one purlin. The other purlin buckled locally in the flange stiffener. (7) ndicated buckling was in the flange stiffener. The other purlin was restrained by the test machine due to large lateral deflections. (8) Flange stiffener buckling. (9) Ends of purlins were fixed. (10) One purlin was tested previously and was badly distorted. Q\ 00

77 69 TABLE 4.1 TEST ULTMATE STRESSES(3) Purlin Yield Vacuum Test Beam Test Type Stress (cry) Stress %cr y Stress %cr y A B 57.6 y(1,2) Y C Y D y E (1) (y) ield (2) (3) Duplicate test (V7) gave of 45.6 ksi (79.2 %cr y ) All stresses are in ksi. ultimate stress

78 70 TABLE 4.2 ROTATONAL RESTRANT FACTORS (F)(2) Vacuum Test Beam Test PURLN Max. Rot. F Max. Rot. F TYPE (rad. ) (rad.) A B C D E.060(1) (1) F not based on this value (see Fig. 4.21). (2) F is in k-in/in/rad.

79 71 TABLE 4.3 ROTATONAL DEFORMATON OF PURLN WEB Purlin Type Hit (8 p /8)v (1) (2) (8 p /8)B A B c D E (1) (2) Ratio of rotational deformation of purlin web (8 ) to total rotation (8) in diaphragm-braced p F tests. Ratio of rotational deformation of purlin web (8 ) to total rotation (8) in channel-braced p F tests.

80 72 TABLE 4.4 YELD AND ULTMATE STRESSES PURLN F F (1) F (2) TYPE Y bw,s bw,u (KS) (KS) (KS) A B C D E (1) Computed using the F bw equation for beams with stiffened compression flanges (Reference 13). F = [ bw (hit) ~] Fy. (2) Computed using the F bw equation for beams with unstiffened compression flanges (Reference 13). F bw = [1.257.OOOS08(h/t) S;]F y.

81 73 SUMMARY TABLE 4.5 OF ANALYSS TYPES() ANALYSS TYPE a b c d e f g h ULTMATE STRESS (2) FLANGE TYPE (3) BASS OF EFFECTVE WDTH(4) ~ F AA Fbw F NA F y S TW F bw S TW ~ S ~ F bw S FW F y.. U TW F bw U TW (1) T~is table deals with the parameters used in the AS Desgn Manual Part Section 3 "type" analyses. Ahll moments of inertias and section moduli were found on t e basis of sharp corners. (2) The stress indicated was substituted for F y required in the Cholumn formulas to be used with the procedure. Fbw were t e web ultimate stresses as listed in Table 4.4 for unftiffened compression flanges since this equation gives ower stresses and hence underestimates the strength. (3) F - Full flange width (unreduced). S - The effective width was determined with the equations given in Appendix B for plate elements with edge stiffeners. U - The effective width was determined with the equations given in Appendix B for unstiffened flanges (with k = 0.7). n this case the width of the flange was taken as the total width of the flange plus the width of the lip. (4) NA - Not applicable full flange width was used. TW - wit was based ~n the full flange width. n all cases, the rlt was greater than 4 for the lip-flange corner, thus possibly justifying the approach. FW - wit was based on the flange flat width. W~en flange effective width was used, the lip effective Wdth determined according to Appendix B was also used. Even when Fbw was used for failure criteria, the effective width was based on F y and not Fbw, thus eliminating a very tedious iterative procedure. This procedure leads to underestimating the capacity.

82 TABLE 4.6 COMPARSON OF OBSERVED AND COMPUTED ULTMATE LOADS N VACUUM TESTS qtest/qcomputed PURLN ANALYSS TYPE(l) TYPE F (a) (b) (c) (d) (e) (f) (g) (h) A B C D E j:::o Mean St. Dev St. Dev. Mean Ultimate Stress F y F bw F Y F bw F Y F bw F y F bw Flange Type F F S S S S U U Basis of eff. w NA NA TW TW FW FW TW TW (l)see Table 4.5 for further information.

83 TABLE 4.7 COMPARSON OF OBSERVED AND COMPUTED ULTMATE LOADS BEAM TESTS (load)t es t/(load) compo PURLN TYPE F (a) (b) (c) (d) (e) (f) (g) (h) A B C D J V E Mean St. Dev St. Dev. Mean Ultimate Stress F y F bw F F bw F F bw F Y Y Y F bw Flange Type F F S S S S U U Basis of eff. w NA NA TW TW FW FW TW TW (l)see Table 4.5 for further information.

84 76 TABLE 4.8 MNMUM STFFENER REQUREMENT ACCORDNG TO AS 1(1) (2) PURLN FLANGE (3) FLANGE (3) STFFENER TYPE WDTH min WDTH min!(4) (in) (in.. ) (in) (in.. ) (~n") A B C D E (1)Tota1 flange width used. (2)F1at flange width used. (3)Minimum stiffener moment of inertia required. (4)Moment of inertia of stiffener.

85 77 TABLE 4.9 EFFECTVE WDTHS OF COMPRESSON FLANGES AND LP-STFFENERS (Desmond Method) PURLN TYPE W(in( S (1) (in) W(in) s(l)(in) (in) A B (2) 0.90(2) C D (2) E Based on total width. Based on flat width. Based on total length of flange + stiffener and considered as unstiffened. (1) Reduced length of partial stiffener unless otherwise noted. (2)Ful1y effective. W = flange width. S = stiffener length.

86 78 FGURES

87 79 oti4inot caftflqutotlon uckle< col#iqutotion FG. 2.1 MODE OF BUCKLNG 6,14.., c: a ; ~ At or.o of CO.,...SSlon FG. 2.2 FORCE NORMAL TO BUCKLED FLANGE 6 r---, , -_... R y h r-- / / / / 1& /--.. FG. 2.3 FORCE NORMAL TO BUCKLED WEB 6,14

88 80 f..... [ JJh or. b., C.ase t Beam with ~ymll1etric flallge'! [ J [. b ~l Case Sheet with ~lilfellen_ymllleiric flanges _JJ_h-1 C.a~.Sheel wilh ~liltcllcr_alllis\lnlllclric f1;la'c~ Sou. i\rrows in,licate prohahle direction of col\ap~ due to sh~r 2, "",. is portion of tension flange 5upporlinl/i weh 5. "h" is distance from tension flange to cenlroid of etluivalenl column FG. 2.4 THREE POSSBLE TYPES OF SUPPORTNG ELASTC FRAME FOR EQUVALENT COLU~m6

89 81 4 ". '+!z.n '.z.....e fl '"..e"," 11+.,..1..,. "~ j UJ -++ l...l- t.s 3 2\- ~. "~..,... '.c- /'-- 1,... '4 ' ' lo U FG. Z.S THE EFFECT OF THE RATO b/h ON R AND S FOR CASE 1 6 LO r L,"'1f'~y'M;S T 100 FG. 2.6 T vs. LENGTH CURVES 6

90

91 83 60" Support member Z - purlin Polyethylene sheeting Vacuum!l J, 'Wooden box frame " J FG. 3.2 SECTON OF VACUUM TEST SETUP

92

93 A,.. L4 1. o... \-0 4' i.. 4 '.\.. ' 4' ' 20' '.! 1\ 1 00 U1.. 16" J Section A-A FG. 3.4 DETALS OF BEAM TEST SETUP

94 86 H FG. 3.5 Z-SECTON DME~SON

95 87,... "l:t N.i-.... Q) tlo t'd C-' '-' Z 0-Eo- U W en en en 0a:= u ~ W ~ ~ Z... <Q.. ~ - ~ or -~... --d- '" l"'l e Co:'- t.t. i... i., ~-

96 88 Pu rl in cross -section,,,,.94{ , --.,.25.:.66,:, \ \ V2 V5,.47: ~ \.;W \, :.91,! \ V3 V6,.31 : :.- \,.56: -e4 \,,, :.31,..-,.12: -:, \ V4 V7 FG. 3.7 NTAL SWEEPS OF COMPRESSON FL~~GES AT MDSPAN N VACUUM TESTS (NCHES).

97 89 Purlin cross - section,.~,,, \ 1 19,-,, \.2~:, \!.39, 83 86,,, :'22.50J.50:,... --,,,,, ,,.O~, FG. 3.8 NTAL SWEEPS OF COMPRESSON FLANGES N BEAM TESTS (NCHES).

98 90 ~ " 4 5 Vacuum tests 8 ~ eam tests FG. 3.9 LOCATON OF STRAN GAGES

99 Purlin Load Ho H L Screw Support 1.0 -' Panel 18" FG F TEST: DAPHRAGM-BRACED PURLN

100 92 Deflection gage Z - purl in A»==-r-F~~--r--""'" P (load) Support / 12" Channel section ~ ~ 12" Load point Z - pur tin ~ Channe section 12" (bolted to bottom Section A-A flange) FG F TEST: CHANNEL-BRACED PURLN

101 93 p -...;;~ Panel ~---b =6.354.; / X / / / / Z - purlins " L-/ ~, y...j / e :-./ --'" Y1-s'-! -Q =10' Legend:, 2, 3: gages Frame - beam Z - purlin welded at F==- ~_~_~_~_~_~_~we b on y Ang.e bracket Frame channel Bolts (at web only) Section X - X Section Y -Y FG SHEAR RGDTY TEST SETUP

102

103

104

105